NotesECN741-page38

# NotesECN741-page38 - Suppose we want to implement this...

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ECN 741: Public Economics Fall 2008 Next we check that under these allocations, the I.C. constraints for type L is slack. v y ( θ H ) θ L - v y ( θ L ) θ L = Z y ( θ H ) y ( θ L ) v y θ L dy > Z y ( θ H ) y ( θ L ) v y θ H dy = v y ( θ H ) θ H - v y ( θ L ) θ H = u ( c ( θ H )) - u ( c ( θ L )) rearrange terms u ( c ( θ L )) - v y ( θ L ) θ L > u ( c ( θ H )) - v y ( θ H ) θ L So, we know that our characterization is valid. Note that under this characterization 1 θ L v 0 y ( θ L ) θ L - u 0 ( c ( θ L )) = μ π ( θ H ) π ( θ L ) 1 θ H v 0 y ( θ L ) θ H - u 0 ( c ( θ L )) < μ π ( θ H ) π ( θ L ) 1 θ H v 0 y ( θ H ) θ H - u 0 ( c ( θ H )) < 0 and hence 1 θ L v 0 y ( θ L ) θ L < u 0 ( c ( θ L )) there is distortion for the low type.
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Unformatted text preview: Suppose we want to implement this allocation with a nonlinear tax function T ( y ) . Let T ( y ) = y-c if y ∈ { y ( θ H ) ,y ( θ L ) } and T ( y ) = y otherwise. Consider the consumer’s problem max u ( c )-v µ y θ ¶ sub. to. c = y-T ( y ) FOC u ( c )(1-T ( y )) = 1 θ v µ y θ ¶ 38...
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